Uniform great rhombicosidodecahedron

In geometry, the uniform great rhombicosidodecahedron is a nonconvex uniform polyhedron, indexed as U₆₇. It is also called the "quasirhombicosidodecahedron".

This model shares the name with the convex great rhombicosidodecahedron, which is also called the "truncated icosidodecahedron". Because of this confusion the word uniform was added to this article name.

It shares its vertex arrangement with the truncated great dodecahedron, and with the uniform compounds of 6 or 12 pentagonal prisms.

Cartesian coordinates

Cartesian coordinates for the vertices of a uniform great rhombicosidodecahedron are all the even permutations of

: (±1/τ², 0, ±(2−1/τ)): (±1, ±1/τ³, ±1): (±1/τ, ±1/τ², ±2/τ)

where τ = (1+√5)/2 is the golden ratio (sometimes written φ).

See also

* List of uniform polyhedra

External links

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